Question: Christopher is 3 times as old as Ishaan. Four years ago, Christopher was 5 times as old as Ishaan. How old is Ishaan now?
Answer: We can use the given information to write down two equations that describe the ages of Christopher and Ishaan. Let Christopher's current age be $c$ and Ishaan's current age be $i$ The information in the first sentence can be expressed in the following equation: $c = 3i$ Four years ago, Christopher was $c - 4$ years old, and Ishaan was $i - 4$ years old. The information in the second sentence can be expressed in the following equation: $c - 4 = 5(i - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to use our first equation for $c$ and substitute it into our second equation. Our first equation is: $c = 3i$ . Substituting this into our second equation, we get: $3i$ $-$ $4 = 5(i - 4)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $3 i - 4 = 5 i - 20$ Solving for $i$ , we get: $2 i = 16.$ $i = 8$.